Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+3y &= 7 \\ 8x-2y &= -4\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = -8x-4$ Divide both sides by $-2$ to isolate $y$ $y = {4x + 2}$ Substitute this expression for $y$ in the first equation. $-5x+3({4x + 2}) = 7$ $-5x + 12x + 6 = 7$ Simplify by combining terms, then solve for $x$ $7x + 6 = 7$ $7x = 1$ $x = \dfrac{1}{7}$ Substitute $\dfrac{1}{7}$ for $x$ back into the top equation. $-5( \dfrac{1}{7})+3y = 7$ $-\dfrac{5}{7}+3y = 7$ $3y = \dfrac{54}{7}$ $y = \dfrac{18}{7}$ The solution is $\enspace x = \dfrac{1}{7}, \enspace y = \dfrac{18}{7}$.